vu (tv2894) – Homework 9 (Quest) – miner – (55096)
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001
10.0 points
Find the value of
f
′
(0) when
f
(
x
) = (1

3
x
)
−
2
.
Correct answer: 6.
Explanation:
Using the chain rule and the fact that
(
x
α
)
′
=
α x
α
−
1
,
we obtain
f
′
(
x
) =
6
(1

3
x
)
3
.
At
x
= 0, therefore,
f
′
(0) = 6
.
002
10.0 points
Find the derivative of
f
when
f
(
x
) =
parenleftBig
x
9
/
2

4
x
−
9
/
2
parenrightBig
2
.
1.
f
′
(
x
) = 9
parenleftbigg
x
18

16
x
10
parenrightbigg
correct
2.
f
′
(
x
) = 9
parenleftbigg
x
18

4
x
9
parenrightbigg
3.
f
′
(
x
) = 10
parenleftbigg
1 + 4
x
−
18
x
9
parenrightbigg
4.
f
′
(
x
) = 10
parenleftbigg
1

4
x
−
18
x
9
parenrightbigg
5.
f
′
(
x
) = 10
parenleftbigg
x
18
+ 16
x
10
parenrightbigg
6.
f
′
(
x
) = 9
parenleftbigg
x
9
+ 4
x
9
parenrightbigg
Explanation:
After expansion,
parenleftBig
x
9
/
2

4
x
−
9
/
2
parenrightBig
2
=
x
9

8 + 16
x
−
9
Thus
f
′
(
x
) = 9
x
8

144
x
−
10
= 9
x
8

144
x
10
.
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 Fall '10
 Gualdini
 Calculus, Derivative, Slope, Cos

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